1.5 Scatter Plots and Least Squares Lines

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Presentation transcript:

1.5 Scatter Plots and Least Squares Lines Objective: To create a scatter plot and draw an informal inference; use your calculator to find the equation for the least squares line.

Scatter Plots

Scatter Plots In many real-world problems, you will find data that relate two variables such as time and distance or age and height. You can view the relationship between two variables with a scatter plot.

Scatter Plots The following data on the number of reported cases of chicken pox in thousands in the United States is graphed in a scatter plot. The variable x represents the number years after 1988 (x = 0 is 1988) and y represents the number of cases in thousands.

Scatter Plots The chicken pox data involves a two-variable data set that has a negative correlation. In general, there is a correlation between two variables when there appears to be a line about which the data points cluster. There are three situations:

Scatter Plots A scatter plot can help you see patterns in data involving two variables. If you think there may be a linear correlation between the variables, you can use a calculator to find a linear-regression line, also called the least-squares line, that best fits the data.

Scatter Plots The graph below shows the vertical distance from each point in a scatter plot to a fitted line. The fit of a least-squares line is based on minimizing these vertical distances for a data set. A least-squares line is one type of linear model for a data set.

Example 1

Scatter Plots First, hit the stat button. This screen should appear.

Scatter Plots First, hit the stat button. This screen should appear. Now, hit enter to choose edit. This screen should appear.

Scatter Plots First, hit the stat button. This screen should appear. Now, hit enter to choose edit. This screen should appear. Now, enter you values for x under L1. After you enter each value, hit enter.

Scatter Plots Select the right arrow key to move to L2. Enter your y values there. Hit enter after each value.

Scatter Plots Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear.

Scatter Plots Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear. Now hit enter and this screen should appear.

Scatter Plots Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear. Now hit enter and this screen should appear. Hit enter again to select on.

Scatter Plots Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear. Now hit enter and this screen should appear. Hit enter again to select on. Hit graph to see the scatter plot.

Scatter Plots Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear. Now hit enter and this screen should appear. Hit enter again to select on. Hit graph to see the scatter plot. Adjust your window to see all values.

Example 1

Scatter Plots Now, select the stat key. Next select CALC. Now, select LinReg(ax+b). Hit enter twice.

Scatter Plots Now, go to y= and enter the equation of the least-squares line.

Example 1

Correlation and Prediction

Correlation and Prediction

Example 2

Example 2

Homework Page 41 13-20 all